Symmetric Matrices & Quadratic Forms · Challenge problem

A quadratic form $q$ on $\mathbb R^2$ has $q(1, 0) = 3$, $q(0, 1) = 5$ and $q(1, 1) = 2$. Find the minimum value of $q(x, y)$ on the unit circle $x^2 + y^2 = 1$.